A two-fluid model for two-phase flow in PEMFCs

In this study, a two-fluid (TF) model is developed for two-phase flows in proton exchange membrane fuel cells (PEMFCs). The drag force and lift force between gas and liquid phase are considered in N-S equations. In addition, a simplified model is introduced to obtain the liquid water droplet detachment diameter on the gas diffusion layer (GDL)/channel interface which involves the properties of the GDL/channel interface (contact angle and surface tension). The TF model and the simplified model for the prediction of water droplet detachment diameter on GDL/channel interface are validated by the comparison between the experimental data and the model results, respectively. The effect of the properties of GDL/channel interface (contact angle and surface tension) on two-phase behavior in PEMFCs is investigated, The results show that a high contact angle and a low surface tension are advantageous for liquid water removal in the gas channel and the GDL even though a low surface tension will lead to a low capillary force in the GDL.     

A dynamic two phase flow model for a pilot scale sodium borohydride hydrogen generation reactor

A two-dimensional, non-isothermal and dynamic model was developed to describe a sodium borohydride/hydrogen reactor for stationary use. All relevant transport phenomena were treated in detail and the kinetic model developed previously by the authors was introduced into the algorithm. In this paper the reactive solution was modelled as a two phase flow; with this approach the impact of the hydrogen production on the solution stirring could be observed and quantified.     

Simplified model for droplet combustion in a slow convective flow

An idealized model for droplet vaporization or combustion in the Burke-Schumann reaction-sheet approximation is analyzed in terms of a Peclet number based on the Stefan velocity, taken to be of order unity, for Lewis numbers of unity and for small values of a parameter ?, defined as the ratio of the convective velocity far from the droplet to the Stefan velocity at its surface. Asymptotic solutions for the velocity, pressure, and mixture-fraction fields are obtained through second order in ?. The results are employed to calculate the effects of convection on the burning rate and on the flame shape. The prediction that the burning-rate constant increases linearly with ? for small values of ? is shown to be consistent with available experimental data. It is demonstrated that reasonable values of diffusivities provide approximate agreement of predicted burning rates and flame shapes with results of measurements.     

Heat transfer coefficients in two phase flow for the water/lithium bromide mixture used in solar absorption refrigeration systems

This paper describes the experimental results obtained from the heat transfer in saturated nucleate boiling for the water/lithium bromide mixture flowing upward in a uniformly heated vertical tube, which is the generator of a solar absorption refrigeration system. The concentration range for the mixture was from 48 to 56 wt.% Plots of local and average heat transfer coefficients are shown against solution concentration, heat flux and the temperature difference between the wall tube and the fluid. It was observed that the average heat transfer coefficients increased for the mixture with an increase of the heat flux and with the decrease of the solution concentration and the temperature difference. The average heat transfer coefficients varied from 1.0 to 4.0 kW/m² °C.     

A fractal model for predicting permeability and liquid water relative permeability in the gas diffusion layer (GDL) of PEMFCs

In this study, a fractal model is developed to predict the permeability and liquid water relative permeability of the GDL (TGP-H-120 carbon paper) in proton exchange membrane fuel cells (PEMFCs), based on the micrographs (by SEM, i.e. scanning electron microscope) of the TGP-H-120. Pore size distribution (PSD), maximum pore size, porosity, diameter of the carbon fiber, pore tortuosity, area dimension, hydrophilicity or hydrophobicity, the thickness of GDL and saturation are involved in this model. The model was validated by comparison between the predicted results and experimental data. The results indicate that the water relative permeability in the hydrophobicity case is much higher than in the hydrophilicity case. So, a hydrophobic carbon paper is preferred for efficient removal of liquid water from the cathode of PEMFCs.     

A hydrodynamic network model for interdigitated flow fields

The flow field is one of the main components of a fuel cell, which distributes the reactants to the active area of the cell and evacuates the products formed. Interdigitated flow field (IFF) is one among the different types of flow field designs that forces the reactants or products to flow through the electrode, thereby increasing the cell performance by decreasing concentration polarization loss, however, at the cost of higher-pressure drop. Prior understanding of the reactant and water vapour distribution in a flow field helps in obtaining the best flow field design. In the present paper, a model for the flow distribution and the pressure drop in an IFF has been developed using the analogy between fluid flow and electrical network in which the pressure is made analogous to the voltage and the flow rate to the current. The model, which ultimately reduces to the solution of a set of simultaneous algebraic equations, is capable of predicting the flow split among a set of inlet and outlet channels of an interdigitated flow field as well as the overall pressure drop for laminar, turbulent and two-phase flow conditions for arbitrary number of parallel channels. The results from the hydrodynamic network model have been validated against CFD simulations. This model can therefore be used for the optimization of interdigitated flow field design.     

A generalized multiphase mixture (M2) model for PEFC flow field design

A lot of effort has gone into designing an optimum flow field for PEFC (Polymer Electrolyte Fuel Cell) that can both efficiently distribute reactants to the reactions sites and remove products through the outlet. Presence of liquid water in the products has been one of the main concerns. Unfortunately, single phase flow solutions have been considered for most of the design optimization studies due to the unavailability of a fast and accurate two-phase flow model. Recently a Multiphase-Mixture (M2) based model has been developed for two-phase flow computations in the cathode channels of a PEFC. This model has now been extended to the anode side. A drawback of implementing this mvodel is that it requires an orthogonal hexahedral mesh which in a real PEFC stack geometry is very difficult to achieve. In this study the model has been extended to non-orthogonal hexahedral and tetrahedral meshes, which can be used to mesh any three-dimensional geometry. Also, in order to reduce the meshing effort, an immersed body approach has been tested successfully on this model. The resulting two-phase flow model valid for arbitrary flow field geometries is fast and accurate and a possible direction to reduce the meshing effort is presented.     

Sensitivity study for the mass transfer at a single droplet

The mass transfer between a single droplet and a surrounding fluid can be described mathematically solving the momentum and mass balances in both phases (conjugate problem). This study of dimensionless parameters shows how the process is influenced by changes in material properties and operating conditions.The influence of the Reynolds number Re on the mass transfer is found to be small and to vanish for creeping flows. A sensitivity to the viscosity ratio μ* exists only in a limited range. The influence of the Peclet number Pe can be approximated for small Pe by considering only the external problem and for high Pe by considering only the internal problem.     

A new analysis of two phase flow on hydrogen production from water electrolysis

It is clear that the entire world have to research, develop, demonstrate and plan for alternative energy systems for shorter term and also longer term. As a clean energy carrier, hydrogen has become increasingly important. It owes its prestige to the increase within the energy costs as a result of the equivocalness in the future availability. Two phase flow and hydrogen gas flow dynamics effect on performance of water electrolysis. Hydrogen bubbles are recognized to influence energy and mass transfer in gas-evolving electrodes. The movement of hydrogen bubbles on the electrodes in alkaline electrolysis is known to affect the reaction efficiency. Within the scope of this research, a physical modeling for the alkaline electrolysis is determined and the studies about the two-phase flow model are carried out for this model. Internal and external forces acting on the resulting bubbles are also determined. In this research, the analytical solution of two-phase flow analysis of hydrogen in the electrolysis is analyzed.     

A three-dimensional two-phase flow model for a liquid-fed direct methanol fuel cell

A three-dimensional, two-phase, multi-component model has been developed for a liquid-fed DMFC. The modeling domain consists of the membrane, two catalyst layers, two diffusion layers, and two channels. Both liquid and gas phases are considered in the entire anode, including the channel, the diffusion layer and the catalyst layer; while at the cathode, two phases are considered in the gas diffusion layer and the catalyst layer but only single gas phase is considered in the channels. For electrochemical kinetics, the Tafel equation incorporating the effects of two phases is used at both the cathode and anode sides. At the anode side the presence of gas phase reduces the active catalyst areas, while at the cathode side the presence of liquid water reduces the active catalyst areas. The mixed potential effects due to methanol crossover are also included in the model. The results from the two-phase flow mode fit the experimental results better than those from the single-phase model. The modeling results show that the single-phase models over-predict methanol crossover. The modeling results also show that the porosity of the anode diffusion layer plays an important role in the DMFC performance. With low diffusion layer porosity, the produced carbon dioxide cannot be removed effectively from the catalyst layer, thus reducing the active catalyst area as well as blocking methanol from reaching the reaction zone. A similar effect exits in the cathode for the liquid water.     

An investigation of water-gas transport processes in the gas-diffusion-layer of a PEM fuel cell by a multiphase multiple-relaxation-time lattice Boltzmann model

In order to study water-gas transport processes in the gas-diffusion-layer (GDL) of a proton exchange membrane (PEM) fuel cell system, a multiphase, multiple-relaxation-time lattice Boltzmann model is presented in this work. The model is based on the mean-field diffuse interface theory and can handle the multiphase flows with large density ratios and various viscosities. By using the standard bounce back boundary condition and an approximate average scheme for the non-slip and wetting boundary walls, respectively, detailed liquid-gas transportation in the GDL, in which exact boundary condition is difficult to be implemented, can be simulated. Unlike most of lattice Boltzmann methods based on the Bhatnagar–Gross–Krook collision operator, the present model shows a viscosity-independent velocity field, which is very important in simulating multiphase flows where various viscosities coexist. We validate our model by simulating a static droplet on a wetting wall and compare with theoretical predictions. Then, we simulate a water-gas flow in the GDL of a PEM fuel cell and investigate the saturation-dependent transport properties under different conditions. The results are shown to be qualitatively consistent with the previous numerical and theoretical works.     

Eulerian approach for multiphase flow simulation in a glass melter

A glass furnace, consisting of a combustion space and a glass melter, uses combustion heat to melt sand and cullet into liquid glass to make products. Glass quality is mainly dependent on the temperature, glass composition, and the level of impurities in a glass melter, which include solid batch/cullet particles, liquid glass, and gas bubbles. A comprehensive computational model using an Eulerian approach has been developed to simulate multiphase flows in a glass melter. It includes all the phases, divides solid particles or gas bubbles into various size groups, and treats each group as a continuum. The derived mass, momentum, and energy conservation equations of the flow are solved for local properties for each phase. The simulation considers the heating and melting of the batch (mainly from the radiative heat from combustion and from the convective heat from the molten glass), the formation and transport of bubbles, and the heating and mixing of the liquid glass. The approach was incorporated into a multiphase reacting flow computational fluid dynamics code that simulates overall glass furnace flows to evaluate the glass quality and furnace efficiency.     

Liquid water transport in gas flow channels of PEMFCs: A review on numerical simulations and visualization experiments

Proper water management in gas flow channels of a proton exchange membrane fuel cell (PEMFC) necessitates a comprehensive understanding of liquid water generation and motion, which are strongly related to droplet dynamics and flow patterns. Based on existing literature on numerical simulations using Volume of Fluid (VOF) method and Lattice Boltzmann method (LBM), this review identifies and analyzes the main factors in detail that affect the droplet dynamics including surface wettability, initial states of liquid water, geometrical structures of channels, and operating conditions. In addition, visualization experiments can effectively compensate for numerical simulations restricted by the limitations of length and time scale. This review focuses on optical photography, which is currently considered as the most convenient and low-cost method and discusses experimental apparatuses, qualitative flow pattern maps, and quantitative information. Finally, strategies for liquid water removal from gas flow channels are extracted to further enhance the performance of low-temperature PEMFCs.     

The effect of slip velocity on saturation for multiphase condensing mixtures in a PEM fuel cell

In this paper, we have developed an approximate formula for liquid saturation within a two phase condensing mixture that relates the saturation level to the slip velocity between the gas and liquid phases. In particular, we have explained why models in which the slip velocity is assumed to be zero exhibit a saturation that is several orders of magnitude smaller than in other models where slip velocity was allowed to vary. This is a discrepancy that has appeared in computed results reported in the fuel cell literature, but which has not yet received a satisfactory explanation. We demonstrate that the reason behind the large discrepancy is rooted in the type of model used to treat the slip velocity between phases.     

Experimental study on the two phase flow behavior in PEM fuel cell parallel channels with porous media inserts

In this study, the air–water two phase flow behavior in PEM fuel cell parallel channels with porous media inserts was experimentally investigated using a self-designed and manufactured transparent assembly. The visualization images of the two phase flow in channels with porous media inserts were presented and three patterns were summarized. Compared with the traditional hollow channel design, the novel configuration featured less severe two phase flow mal-distribution and self-adjustment to water amount in channels, although a higher pressure drop was introduced due to the porous media inserts. The dominant frequency of pressure drop signal was found to be a diagnostic tool for water behavior in channels. The novel flow channel design with porous media inserts may become a solution to the water management problem in PEM fuel cells.     

气固两相旋流中气粒两相流场特性数值模拟

以气固旋流分离器为研究对象，对气相采用κ-ε模型及代数应力模型，对颗粒相应用随机轨道模型，并考虑相间耦合的相互作用，建立了描述气固两相旋流中气粒两相流场特性数学模型，同时，应用SIMPLEC方法，成功地进行了气固两相旋流听敢粒两相流场特性数值模拟。结果表明：在内锥体顶部上方易形成旋涡；分离器靠外壁处气流为上升流，且偏向出口；在分离器中心区域存在回流，越靠近底部，回流越明显；尘粒初始位置越靠近分离器入口断面底部与分离器外侧越易到达分离器底部；在相同初始条件下，较大粒径尘粒易于到达分离器底部，较小粒径尘粒则先向分离器底部运动，后又向分离器顶部运行，从而可能从分离器出口跑出，或在分离器中某一位置不停旋转。     

A practical Equivalent Electrical Circuit model for Proton Exchange Membrane Fuel Cell (PEMFC) systems

An alternative Equivalent Electrical Circuit for Proton Exchange Membrane Fuel Cells is modelled in this study. Both I–V characteristics and H₂ consumptions corresponding to generated power under load and no-load conditions are investigated. For this purpose, H₂ consumptions and I–V characteristics of three different sized PEMFCs are tested. There is a very good harmony between the model results and measured values (relative error %0.7, %6.4 and %2.5 for FC-A, FC-B and FC-C respectively). In the proposed model current passes only on parallel resistance and not on serial resistance at no-load condition. Thus, a FC with higher parallel resistance should be preferred. Another key output of this study is that based on the proposed model, performance comparison of FCs can be performed with the parameters defined in this work. Proposals made in this study can easily be used for performance analysis of FCs under for both steady state and transient analysis.     

Drift-flux model for downward two-phase flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for downward two-phase flows. The constitutive equation that specifies the distribution parameter in the downward flow has been derived by taking into account the effect of the downward mixture volumetric flux on the phase distribution. It was assumed that the constitutive equation for the drift velocity developed by Ishii for a vertical upward churn-turbulent flow determined the drift velocity for the downward flow over all of flow regimes. To evaluate the drift-flux model with newly developed constitutive equations, area-averaged void fraction measurement has been extensively performed by employing an impedance void meter for an adiabatic vertical co-current downward air-water two-phase flow in 25.4-mm and 50.8-mm inner diameter round tubes. The newly developed drift-flux model has been validated by 462 data sets obtained in the present study and literatures under various experimental conditions. These data sets cover extensive experimental conditions such as flow system (air-water and steam-water), channel diameter (16-102.3 mm), pressure (0.1-1.5 MPa), and mixture volumetric flux (−0.45 to −24.6 m/s). An excellent agreement has been obtained between the newly developed drift-flux model and the data within an average relative deviation of ±15.4%.     

Update on numerical model for the performance prediction of a PEM Fuel Cell

A Computational Fluid Dynamics (CFD) model developed for a 50 cm² Fuel Cell with parallel and serpentine flow field bipolar plates was presented in an article published in the International Journal of Hydrogen Energy 35 (2010) 11,533-11,550 [1]. The experimental validation details were presented as well in an article published in the International Journal of Hydrogen Energy 35 (2010) 11,437-11,447 [2]. A good agreement between numerical results and experimental measurements were obtained except for the high current density region where mass-transport limitations dominate the voltage loss. This short communication presents an update on the last simulations performed, where an improved prediction of the polarization curve is obtained. The physical and computational aspects of the reasons underlying the improvement of the results are discussed.     

Applications of Electrical Capacitance Tomography in Two Phase Flow Visualization

The successful application of Electrical Capacitance Tomography (ECT) depends heavily on the image reconstruction speed and quality. The two requirements usually cannot be satisfied simultaneously. Also, for a large number of acquired 2D ECT images, a 3D presentation of them is much desired to track the variations of the material distribution in a third dimension. To facilitate ECT for practical flow analyses in process engineering, the authors have recently developed algorithms for 3D image presentation and for online iterative image reconstruction that only takes the same time as a linear back projection method but yields good image qualities as the Landweber iterative method does. The new methods have been successfully applied to visualize several classes of two phase flows, namely fluidization, cyclone separation, circulating rate determination in circulating fluidized beds, pneumatic conveying, rotating drum mixing. Special characteristics in each case have been discussed and valuable results are obtained, which are reported in this paper.